Stability of capture into parametric autoresonance |
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Authors: | O A Sultanov |
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Institution: | 1.Institute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences,Yekaterinburg,Russia |
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Abstract: | We consider nonlinear elliptic second-order variational inequalities with degenerate (with respect to the spatial variable) and anisotropic coefficients and L 1-data. We study the cases where the set of constraints belongs to a certain anisotropic weighted Sobolev space and to a larger function class. In the first case, some new properties of T-solutions and shift T-solutions of the investigated variational inequalities are established. Moreover, the notion of W 1,1-regular T-solution is introduced, and a theorem of existence and uniqueness of such a solution is proved. In the second case, we introduce the notion of T-solution of the variational inequalities under consideration and establish conditions of existence and uniqueness of such a solution. |
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